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HEAVENLY MATHEMATICS
GEK 1506
Sun and Architecture
Group 66
Lee Jin You, Roger
Lee Ji Hao, Theophilus
Lim Guang Yong
Lim Ghim Hui
Lim ShuEn Adele
Lim Wee Kee
U024711R
U024730X
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U024718X
U024757W
U024699E
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TABLE OF CONTENTS
1.0
2.0
3.0
4.0
Introduction
1.1
Rotation
1.2
Revolution
1.3
Equinox
1.4
Solstice
1.5
Season
1.6
Sun’s apparent motion
Sun Path
2.1
Factors affecting changes in Sun Path
2.2
Sun Path Diagrams
2.3
Effects of Sun Path
2.4
Shade Dial
Sunlight and Architectural Design
3.1
Sunlight as a source of lighting
3.2
The shading effect
3.3
The sun as a source of heat
Sundials
4.1
5.0
Polar Sun Dial
Heliodon
5.1
Introduction
5.2
Sunlight Heliodons
5.3
Artificial Light Heliodons
5.4
Usefulness
5.5
Theory and Application of Our Model
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SUN AND ARCHITECTURE
1.0
INRODUCTION
The sun is the brightest star in the Earth’s solar system. Not only does the sun give us
light, but is also a valuable source of heat energy. The sun can be considered the ‘life
giver’ of all living things on Earth, for without the sun, many living organisms would
cease to exist. However, the sun does create some problems for us. For example,
extreme heat is undesirable as it may cause a sudden increase in bodily temperature.
Hence, people have always sought ways to harness the sun’s power and yet at the same
time reduce the detrimental effects of it. Before explaining the part on how architects
come up with designs of buildings to control the sun’s energy, it is important to give a
short summary of the relationship between the sun and the earth as this will affect the
architects’ knowledge of the sun’s effect on building design.
1.1
ROTATION
The Earth rotates about on a fixed plane that is tilted 23.5° with respect to its vertical axis
around the sun. The Earth needs 23hrs 56mins to complete one true rotation, or one
sidereal period, around the sun. A sidereal day (period) is the time taken for a given
location on the earth which is pointing to a certain star to make one full rotation and
return back pointing to the same star again. Since the speed of the Earth’s rotation is
constant throughout the year, the Earth’s sidereal day will always be 23hrs 56mins. The
solar day, on the other hand, is the time needed for a point on earth pointing towards a
particular point on the sun to complete one rotation and return to the same point. It is
defined as the time taken for the sun to move from the zenith on one day to the zenith of
the next day, or from noon today to noon tomorrow. The length of a solar day varies, and
thus on the average is calculated to be 24hrs. In the course of the year, a solar day may
differ to as much as 15mins. There are three reasons for this time difference. Firstly it is
because the earth’s motion around the Sun is not perfect circle but is eccentric. The
second reason is due to the fact that the Sun’s apparent motion is not parallel to the
celestial equator. Lastly, the third reason is because of the precession of the Earth’s axis.
For simplicity, we averaged out that the Earth will complete one rotation every 24hrs
(based on a solar day) and thus moves at a rate of 15° per hour (one full rotation is 360°).
Because of this, the sun appears to move proportionately at a constant speed across the
sky. The sun thus produces a daily solar arc, which is the apparent path of the sun’s
motion across the sky. At different latitudes, the sun will travel across the sky at different
angles each day. Greater detail about this phenomenon will be touch on in the later part
of the section.
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The rotation of the earth about its axis also causes the day and night phenomenon. The
length of the day and night depends on the time of the year and the latitude of the location.
For places in the northern hemisphere, the shortest solar day occurs around December 21
(winter solstice) and the longest solar day occurs around June 21 (summer solstice)
(Figure 1.2). In theory, during the time of the equinox, the length of the day should be
0equal to the length of the night. This will be further discussed in the later part too.
Figure 1.1 Different angles of the sun
1.2
REVOLUTION
It is generally accepted that the earth’s complete revolution around the Sun is 365 days.
However, to be exact, the number of days the earth takes to revolve around the sun
actually depends on whether we are referring to a sidereal year or a tropical (solar) year.
A sidereal year is the time taken for the earth to complete exactly one orbit around the
Sun. A sidereal year is then calculated to be 365.2564 solar days. A tropical year is the
time interval between two successive vernal equinoxes, which is 365.2422 solar days.
The difference between the two is that tropical year takes into consideration precession
but the sidereal year does not. Precession is the event where the earth’s axis shifts
clockwise in circular motion which then changes the direction when the North Pole is
pointing.
The difference between the sidereal and the tropical year is 20mins. This difference is
negligible in the short run, but in the long run will cause time calculation problems. Thus
readjustments to calendars must be made to correct this difference. Hence for simplicity,
the average time the earth takes to move around the sun in approximately 365 days. This
path that the earth takes to revolve around the sun is called the elliptical path.
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Spring (Vernal) Equinox
Summer solstice
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Winter solstice
Autumnal (Fall) Equinox
Figure 1.2 Solstices and Equinoxes
1.3
EQUINOX
To explain solstices, equinoxes and season, it will be easier if we use the heliocentric
model. Equinoxes happen when the ecliptic (sun’s apparent motion across the celestial
sphere) and celestial equator intersect. When the sun is moving down from above the
celestial equator, crosses it, then moves below it, that point of intersection between the
two planes is when the Autumnal Equinox occurs. This usually happens around the 22nd
of September. When the Sun moves up from below the celestial equator to above it, the
point of intersection between the sun and the celestial equator is when Spring (Vernal)
Equinox occurs. It usually happens around the 21st of March. During the equinoxes, all
parts of the Earth experiences 12 hours of day and night and that is how equinox gets it
name as equinox means “equal night”. At winter solstice (Dec), the North Pole is inclined
directly away from the sun. 3 months later, the earth will reach the date point of the
March equinox and that the sun’s declination will be 0°. 3 months later, the earth will
reach the date point of the summer solstice. At this point it will be at declination -23.5°.
This cycle will carry on, creating the seasons that we experience on earth (Figure 1.2).
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SOLSTICE
The earth is tilted 23.5o, so is the ecliptic, with respect to the celestial equator, therefore
the Sun maximum angular distance from the celestial equator is 23.5°. At the summer
solstice which occurs around 21st of June, the North Pole is pointing towards the sun at an
angle of 23.5o as shown in figure 1.3. Therefore the apparent declination of the sun is
positive 23.5o with respect to the celestial equator. At the Winter solstice which occurs
around 21st December, the North Pole is pointing away from the sun at an angle of 23.5o.
Therefore the apparent declination of the sun is negative 23.5o with respect to the
celestial equator.
1.5
SEASON
Seasons are caused by the Earth axis which is tilted by 23.5o with respect to the ecliptic
and due to the fact that the axis is always pointed to the same direction. When the
northern axis is pointing to the direction of the Sun, it will be winter in the southern
hemisphere and summer in the northern hemisphere. Northern hemisphere will
experience summer because the Sun’s ray reached that part of the surface directly and
more concentrated hence enabling that area to heat up more quickly. The southern
hemisphere will receive the same amount of light ray at a more glancing angle, hence
spreading out the light ray therefore is less concentrated and colder. The converse holds
true when the Earth southern axis is pointing towards the Sun. (Figure 1.5)
Figure 1.5 Tilt of the earth
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SUN’S APPARENT MOTION
From the heliocentric point of view, the Earth rotates and revolves around the sun in a
counter clockwise direction. However, when we look at the Sun on earth, it appears to be
moving in a clockwise direction. This phenomenon is known as the apparent motion of
the sun.
2.0
SUN PATHS
2.1
INTRODUCTION
Have you ever wondered why the sun rises in the east and sets in the west? For centuries,
this natural phenomenon has always amazed mankind. Being the closest star to us, the
sun certainly brings about a great interest for everyone to study its movement and
behavior, especially its position at different times of the day and month during the year.
However, we first have to understand that viewing the sun from different locations on the
earth, the sun will rise and set from a different point on the horizon and move along
different paths across the sky.
Though knowing that the sun rises in the east and set in the west, do you know that the
sun does not rise exactly due east or sets exactly due west? Instead the sun may rise
further north of east or further south of east, depending on which part of the earth you are
at. To understand where you stand on the earth, it is specified by the latitude and
longitude coordinates.
.
On a globe model, lines of latitude are circles of different sizes. The largest circle is the
equator, whose latitude is zero, while at the poles- at latitudes 90° north and 90° south (or
-90°), the circles shrink to a point as shown below (Figure 2.1a). Whereas for longitude
they are lines, or arcs, extend from pole to pole as shown in the diagram below (Figure
2.1b).
S
Figure 2.1a Lines of Latitude
Figure 2.1b Lines of Longitude
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The base values for the latitude and longitude are the equator and the prime meridian
respectively. The latitude and longitude will have significant effects on the sun path and
hence affects the behavior of the sun’s lighting and heating characteristics.
After explaining the latitudes and longitude, we are going to position ourselves, as
observers to be in the latitude of 0 degree and 90 degrees North. Now looking from an
observer’s point of view, we will try to measure the position of the sun with reference to
the horizon.
To measure the angle of the sun in its motion across the sky, we need to take its altitude
and azimuth reading. Altitude is the angular distance above the horizon measured
perpendicularly to the horizon. It has a maximum value of 900 at the zenith, which is the
point overhead. Azimuth the angular distance measured along the horizon in a clockwise
direction. The number of degrees along the horizon corresponds to the compass direction.
Azimuth starts from exactly north, at 0 degrees, and increases clockwise. The example
below illustrates the sun angles for 56 degrees North latitude (Northern Hemisphere). The
altitude as you can see from the figure below is symbolized by β starts from the horizon
while the azimuth is symbolized by α which starts from the South Pole and travels
clockwise.
β = Altitude
α = Azimuth
β
β
Horizon
Figure 2.1c Azimuth and Altitude
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FACTORS THAT CAUSES THE CHANGE IN SUN PATHS
Figure 2.2a
Figure 2.2b
Depending on the day of the year and the latitude of the observer, it affects where the sun
exactly rises or sets, or how long the sun is above the horizon. As seen from the 2
diagrams above the sun does not necessarily rise due East or set due west. The location of
the sun in the sky is described as having two components: its daily movement around the
horizon and its height above the horizon (altitude). Its altitude varies with the seasons and
location of the observer. At 40 degrees latitude, Figure 2.2a, during the equinox the sun
rises due east, while during solstices the sun rises due south east or north east. At 65
degrees latitude, Figure 2.2b, the sun rises further south of east during the winter solstice
and further north of east during the summer solstice.
The sun’s daily path across the sky on or about the 21st day of each month is indicated by
means of seven curved lines. The path is highest in June and the lowest in December. The
sun travels across the earth’s sky along 7 main paths. Each of the other five paths is for
two months in the year. For instance, the path on the March 21 is the same as on
September 23.
We observe the sun in the northern hemisphere with regards to its paths. The tilt of the
earth causes the seasons which constitutes the difference in the sun paths.
The sun paths are different due to factors such as the:
1) Location (local latitude)
2) Rising and setting position (based on the time of the year)
3) Duration of the day and night
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Figure 2.2c The sun in the sky in the northern hemisphere
During the summer solstice, on the 21st of June, the sun will be traveling at the highest
path across the sky (shown as the red line). In the morning, the sun will rise due north of
east, then crosses the meridian due south at noon and setting a little due north of west.
The duration of the day is longer relative to the night as the sun across the sky. The sun’s
maximum altitude will occur at noon (calculated by the latitude of the observer’s location
plus 23.5o).
Each day the path of the sun becomes lower until the day when the duration is exactly 12
hours; this will be the September equinox, 21st September (shown as purple line). The sun
will rise at exact east and set at exact west.
The sun path is the lowest in the sky during the winter solstice. The sun will rise south of
East and set at the south of West in any of the day in that time of the year. It reaches
nearest to South at noon. The duration of the day will be much shorter relative to the
Summer Solstices and September Equinox. As the earth proceeds into the March equinox,
the altitude of the sun will gradually be higher. The duration of the day will increase to
eventually 12 hours at the equinox (shown as purple line above).
The ever changing path of the Sun is a result of our seasons. The earth as a whole
receives the same amount of sunlight everyday and every year. The apparent movement
of the sun around the earth is relative and due to the earth’s rotation and orbit. The
seasonal differences in the daily path of the sun are due to the tilt of the earth’s axis.
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SUN PATHS DIAGRAM
Sun path diagrams are a convenient way of representing the annual changes in the path of
the Sun through the sky on a single 2D diagram. Their most immediate use is that the
solar azimuth and altitude can be read off directly for any time of the day and month of
the year. They also provide a unique summary of solar position that the architect can refer
to when considering shading requirements and design options. There are quite a few
different types of sun-path diagrams, however, we will only examine two main forms.
The Stereographic Diagrams
Stereographic diagrams are used to represent the sun's changing position in the sky
throughout the day and year. In form, they can be likened to a photograph of the sky,
taken looking straight up towards the zenith, with a 180° fish eye lens. The paths of the
sun at different times of the year can then be projected onto this flattened hemisphere for
any location on Earth.
A basic full stereographic diagram, with all its components is shown below.
Source: www.squ1.com/solar/sun-path-diagrams.html
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Azimuth Lines and Altitude Lines
Azimuth angles run around the edge of the diagram in 15° increments. A point's azimuth
from the reference position is measured in a clockwise direction from True North on the
horizontal plane. True North on the stereographic diagram is the positive Y axis (straight
up) and is marked with an N.
Altitude angles are represented as concentric circular dotted lines that run from the
centre of the diagram out, in 10° increments from 90 to 0. A point's altitude from the
reference position is measured from the horizontal plane up.
Date Lines and Hour Lines
Date lines represent the path of the sun through the sky on one particular day of the year.
They start on the eastern side of the graph and run to the western side. There are twelve
of these lines shown, for the 1st day of each month. The first six months are shown as
solid lines (Jan-Jun) whilst the last six months are shown as dotted (Jul-Dec), to allow a
clear distinction even though the path of the Sun is cyclical.
Hour lines represent the position of the sun at a specific hour of the day, throughout the
year. They are shown as figure-8 type lines (Analemma) that intersect the date lines. The
intersection points between the date and hour lines give the position of the sun. Half of
each hour line is shown as dotted, to indicate that this is during the latter six months of
the year.
Reading the Sun Position
The position of the Sun in the sky at any time of the day on any day of the year can be
read directly from the diagram above. First you need to locate the required hour line on
the diagram. Then locate the required date line, remembering that solid are used for JanJun and dotted lines for Jul-Dec.
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Follow the steps below to read the Sun position from a stereographic sun-path diagram:
ƒ
Step 1 - Locate the required hour line on the diagram.
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Step 2 - Locate the required date line, remembering that solid are used for JanJun and dotted lines for Jul-Dec.
ƒ
Step 3 - Find the intersection point of the hour and date lines. Remember to
intersect solid with solid and dotted with dotted lines.
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Step 4 - Draw a line from the very centre of the diagram, through the intersection
point, out to the perimeter of the diagram.
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Step 5 - Read the azimuth as an angle taken clockwise from North. In this case,
the value is about 62°.
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Step 6 - Trace a concentric circle around from the intersection point to the vertical
North axis, on which is displayed the altitude angles.
ƒ
Step 7 - Interpolate between the concentric circle lines to find the altitude. In this
case the intersection point sits exactly on the 30° line.
This gives the position of the sun, fully defined as an azimuth and altitude.
Cylindrical Diagrams
A cylindrical projection is simply a 2D graph of the Sun position in Cartesian coordinates. The azimuth is plotted along the horizontal axis whilst the altitude is plotted
vertically. Reading off positions is simply a matter of reading off the two axis, as shown
below.
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Follow the steps below to read the Sun position from a cylindrical sun-path diagram:
ƒ
Step 1 - Locate the required hour line on the diagram.
ƒ
Step 2 - Locate the required date line, remembering that solid are used for JanJun and dotted lines for Jul-Dec. In these diagrams, the highest altitude line at
noon is always in midsummer (either 1st July or 1st Jan, depending on
hemisphere). Each other line represents the 1st of each month, solid Jan-Jun,
dotted Jul-Dec.
ƒ
Step 3 - Find the intersection point of the hour and date lines. Remember to
intersect solid with solid and dotted with dotted lines.
ƒ
Step 4 - The azimuth is given by reading off the horizontal axis. In this case, the
value is about 62°.
ƒ
Step 5 - The altitude is given by reading off the vertical axis. In this case the
intersection point sits almost exactly on the 30° line.
2.4
The Shade Dial
With the shade dial, the shading effect or insolation can be determined on the models at
any geographical location and at any given time. By placing the shade dial near and on
the same surface with the model, we will be able to orientate them as related to the light
source so that the actual position of the insolation will be produced.
Stick with a
rounded head
Time
Month/ date
Semicircular
dial
Knob
Stand
Shadow
(Date and Time)
Figure 2.4 Shade Dial
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The shade dial is made of mainly a semicircular dial, a stick with a rounded head, a on
the side of the dial and a stand.
The semicircular dial is calibrated for the seasonal and hourly changes and is indicated on
the surface of the dial itself. On the dial, it shows the hours of the day and the days of the
month according to the declination of the sun (23.5o). The hour lines of the dial are
marked at 150 intervals hourly due to the rotation of the earth as discussed above. As for
the date lines, they are divided into 3 per month, approximately an interval every 10 days
or on the 1st, 11th and the 21st.Due to the nature of the sun path, each date line will
represent 2 dates (except for the solstices) when the declination of the sun is the same.
For example, 21st February will share the same date line as 21st October. That is why the
date lines run from December to June (top down) on the left side of the shade dial and run
from June to December (bottom up) on the right.
However, the indication is not very exact because of the irregularities between the
astronomical data and the calendar year (shown in the table below). The difference is
very small that is why it is negligible.
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The stick with rounded head is fitted at the center of the dial. Once illuminated, it will
cast a shadow on the dial. The shadow cast will show the month and the time of the day
on the dial, which will correspond to the situation of the sun at that particular time. On
the other hand, if we are interested in the insolation at a particular day and time, we could
adjust accordingly and we will see the illumination of the model eventually.
The knob on the side of the dial is to adjust the position as to simulate the difference in
the geographical location (latitude). Thus the shade dial is usable in any latitude. When
the knob shows “North latitude”, it refers to the northern hemisphere. Thus the knob must
be turned to the correct latitude to simulate the actual location of the land.
The shade dial is usable in both the day time as well as the night time. To measure during
the night, simply turn the shade dial 1800 and the south signal will be parallel to the
model. The shade dial not only makes the study of the distribution of shade and sunshine
possible, but it is also capable of showing the insolation is necessary or not. The shade
dial is able to show us whether the period is “under heated” or “overheated”. The shade
dial can be used as a chart, with the hour line as abscissa and the seasonal declination as
the ordinate. The overheated area will be translated onto the chart. Therefore, the shade
dial is able to determine the direction of shading and able to show us whether the shading
on the building is desirable or not. Same as above, the date lines represent 2 dates in a
year. Therefore, overheated period are area that have darker tones so shading is required
for both the dates. As for the lighter tones, shading is required for only one of the dates.
Darker
tones
Lighter
tones
When setting up the shade dial, much care must be emphasized on the orientation of the
shade dial and the model; both are facing the same direction. For an example, the south
sign of the model must be parallel to the sign indicated on the knob.
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As shown in the figure above, the angle of the shade dial is equal to the geographical
location of the model. For example, tilting of knob to 45o represents the latitude 45o.
Figure 2.4.1 Shade dial and Model of house
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SUNLIGHT AND ARCHITECTURAL DESIGNS
Mankind has always sought ways to harness the power of the sun for their daily needs
and uses. In designing buildings and structures, architects have constantly focused their
attention towards the sun. The sun has been both a bane as well as an aid for building
designers: too much sunlight will lead to excessive heating. On the other hand,
incorporated properly into the design of the building, sunlight can be used as a
complement to light interior facades and rooms. Hence architects today must not only
design buildings to collect energy from the sun to provide heating and lighting, but also
to reject solar energy when is can lead to overheating of the building. This is known as
passive solar architecture. Passive solar design main goals are to reduce the fossil fuel
consumption of buildings as well as produce buildings that act in conjunction with
natural forces and not against them.
This report aims to explain how architects, based on their knowledge of the sun and the
sun’s path, design a building so that the building can fully utilize the available solar
energy. We will discuss three aspects of passive solar design: the lighting consideration,
the shading consideration and the heating consideration. These 3 aspects largely affect
the overall performance of the building in terms of occupational and functional
requirements.
3.1
Sunlight as a source of Lighting
On a clear and bright day, the sun, combined with the reflective qualities of the clear sky,
gives off about 8,000 to 10,000 footcandles of light. During any normal day, be it
overcast or clear, there is almost always enough light available from the sun and sky to
provide illumination for most human visual tasks. However, due to constantly changing
cloud cover, the amount of illumination varies from time to time. Hence it is almost
impossible to predict with precision what the interior daylighting conditions in any
building will be like at any given moment. Nonetheless, the architect should at least have
on hand a rough range of expected daylight conditions based on the sun’s behavior at that
particular location.
The main aims in daylighting a building are to (1) get significant quantities of daylight as
deep into the building as possible, (2) to maintain a uniform distribution of daylight from
one area to another, and (3) to avoid
visual discomfort and glare. Along with
these objectives in mind, the architect
will design a building according to the
sun’s behavior at that particular latitude.
The two main ways architects control the
effects of the sun on the building is
through the orientation of the building
and the overall design structural layout.
Figure 3.1 Daylighting within a building
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First and foremost, sunlight can only be used as a complement to artificial lighting and
not as a main source of light. It is up to architects to design buildings so as to capture as
much sunlight as possible and thus reduce the amount of energy consumption. Depending
on the function of the building, the building may or may not be orientated to face the sun.
For example, most residential buildings are orientated away from the east-west axis as the
rays from the low morning and evening sun can penetrate directly into the building and
cause glare discomfort. On the other hand, commercial buildings may be orientated to
capture these long sun rays for aesthetical reasons.
Another way architects can control the amount of daylighting in a building is through the
actual design structure of the building itself- the use of structural designs and concepts to
allow sunlight penetration. Sometimes buildings are designed with large glass facades to
allow maximum sunlight penetration into the building, and these facades are usually
orientated to slightly face the sun. For most residential buildings, openings such as doors
and windows are preferably not placed along the east-west axis. In commercial buildings,
certain areas are left empty on purpose so that sunlight is allowed into the building
envelope with minimum obstructions. Take for example a museum with a sky vault in
the northern hemisphere. During the summer months when the sun is high in the sky, the
sun will be able to shine directly into the building through the sky vault. But during the
winter months, depending on the size of the sky vault, the sun may not be able to shine
directly onto the museum’s floor. Hence there may be a need to increase artificial
lighting for the various exhibits in the museum. This is a factor that architects may have
to consider when designing the museum.
3.2
The Shading Effect
The sun will always cast a shadow on any object. Only the length, shape and size of the
shadow will change with respect to the sun’s position in the sky throughout the year.
When designing buildings, it is important to notice the amount of shade cast on the
building, or otherwise how its shadow will affect its surroundings. As mentioned earlier
above, at different latitudes, the sun will
travel along different paths across the sky at
different times of the year. The sun’s
peculiar behavior is a very important factor
when designing and constructing buildings.
For locations which are at latitudes away
from the equator, during the summer months,
the sun will cast relatively short shadows
while during the winter months, the sun will
cast long shadows of objects. In the
equatorial region, the sun’s path remains
relatively unchanged hence the length of the
shadows does not vary much throughout the
year.
Depending on the function of the building,
Figure 3.2.1 Shading Devices
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sunlight is either filtered out or allowed to penetrate into the building envelope. Most of
the time, sunlight is filtered out or prevented from reaching the interior facades of the
building. This is done by using three main methods of shading: using natural devices,
internal devices, and external devices. Natural devices include shading by trees and
shrubs. For example, deciduous plants have the advantage of providing shade during the
winter and spring months- most trees give shade only during summer and early autumn as
they shed most of their crown during the winter and spring. During the winter months
(sun is low in the sky), these trees are able to block out the low rays and hence effectively
shading the building. Internal devices include curtains and blinds that are installed within
the building itself. These devices are able to give occupants flexibility as to how much
sunlight is allowed into the building because the occupants are able to physically control
theses devices. Lastly, external devices include structural elements such as overhangs
and louvers that are fixed to the building during construction. These devices are
permanent and hence will have different effective shading qualities as the sun’s position
in the sky is constantly changing. In closing, architects can make use of these 3 devices
to effectively shield the building from the sun’s rays.
With regards to the shadow that the building will cast on its surroundings, this is
determined using a heliodon. This further explained in the next section. An entire model
city landscape is constructed and is then subjected to testing against different angles of
light. The effect of the shadow cast on the surrounding areas is very evident. From there,
architects are able to determine shading effects on different buildings.
3.3
The sun as a heat source
Lastly, the sun is a valuable source of heat energy. Similar to light, the sun’s natural heat
may be wanted or unwanted. Countries in the tropics do not want excessive heating from
the sun while higher latitude countries welcome the sun’s warmth during the winter
months. Hence, the amount of heating required depends largely again on the latitude and
the function of the building. Once again, the orientation of the building as well as the
structural elements used in the design of the building play an active role in controlling the
sun’s heat. For example, buildings with overhangs are able to provide shade during the
summer months- the sun is unable to reach within the building. However, during the
winter months, the sun is allowed to penetrate through the building envelope.
Figure 3.3 Different angles of
the sun
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SUNDIALS
One of the oldest techniques to know the time
is the direct observation of the sun to get its
height or the direction above special landmarks.
This is by means of using sundials.
The sundial dates back to the Egyptian Period,
around 1500 B.C. It was also used in ancient
Greece and Rome. The ancient Eyptians
created simple sundials. These sundials were
built with two boards which were put together
to form a fallen “L” (Figure 4.0) so that the
Figure 4.0 “L” shaped sundial
smaller board could throw a shadow on to the longer
one. The marks on the horizontal board measures the
time. In 1500 BC the ancient Egyptians created simple sundials. In central Europe it was
the most commonly used method to determine the time, even after the mechanical clock
was developed in the 14th century. The sundial was actually used to check and adjust the
time on mechanical clocks until late into the 19th century where the sundials get better
and a new science was created: the Gnomonic science of sundials.
The Greek word gnomon means something like judger (of the time). There are different
types of sundials. The four most popular ones are the horizontal sundial, the vertical
sundial, the equatorial sundial and the polar sundial. All that kinds of sundials have one
thing in common; the angle of inclination of the gnomon (Gn) is always equal with the
latitude (f) of place.
The polar sundial is selected to for use in our experiment to observe the effects of the
sun’s movement on the design and orientation of architectural buildings because of its
ability to tell the time of the day as well as the month of the year.
4.1
The Polar Sundial
The Earth rotates on a tilted axis and the speed of its orbit changes, the sun appears to
move across the sky at slightly different rates throughout the year. This means that the
time is measured by a sundial can be up to 16 minutes faster or slower than the time
measured by a clock. To establish a move uniform unit of time, an average or Mean Solar
Day was adopted.
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The gnomon or style (which casts the shadow) is the "oxhead" in the centre of the dial. At
6 am, the shadow from the top of the gnomon just skims the top of the left hand side of
the sundial. By 6.45am the shadow has traversed, and arrived on the main dial plate. It
slowly moves across the dial. At noon, the sun is directly overhead, and the shadow is
immediately below the gnomon in the centre of the dial plate and finally reaches the end
of the dial plate at around 6pm. The hour markers on this type of sundial are very
unevenly spaced. The formula is h / x = tan(hour angle), where 'h' is the hour and 'x' is
the position on the X-axis.
The latitude can be adjusted by moving the two plates which shows the angles on both
‘ears’ of the dial plate according to the desired latitude. It is best to tilt the model no more
than necessary. Depending on the desired location on the Earth (Northern or Southern
Hemisphere), the polar sundial have to flipped accordingly.
Gnomon
Month
Northern
Hemisphere
“Ear”
Time of
the day
Fig 4.1 A handmade polar sundial
This is a small scale polar sundial used in building and arhictecture decisions making.
There are many other big scale polar sun dials which measures time more accurately in
the world. Below are some of the polar sun dials found in other parts of the world.
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A polar sundial designed by Piers Nicholson
The Greenwich polar sundial
A commercial sun dial
5.0
HELIODON
5.1
Introduction
Heliodons or “sun machines" are developed for the testing of sunlight effects on physical
models, aiming at reproducing the actual direction of sunlight in relation to a building.
Typically these studies seek to examine shading devices that eliminate direct sun from
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areas where visual tasks are critical. Direct sun can cause problems of heat gain and
debilitating glare.
History
The earliest report of heliodon (Fig. 1) was
made by Dufton and Beckett of Building
Research Station of UK in RIBA Journal of 16
May 1931.
In this D & B heliodon, the sunlight direction
for various days was simulated with a lamp to
be fixed at various positions of a vertical lamp
holder. The model was placed at a tilted
platform adjusted for the desired latitude at
which the modeled building was built. The
tilted platform is hinged at an angle = (90°latitude angle) from a horizontal rotating plate.
The rotating plate is marked with a circular
scale of 24 hours for selecting the hour required
for model testing. This plate rotates about a
vertical axis parallel to the vertical lamp holder.
Fig. 1 a D & B heliodon
Over the years heliodons have been built in a variety of configurations. In each case, the
device creates the appropriate geometrical relationship between an architectural scale
model and a representation of the sun. Heliodons are used to simulate the lighting
conditions at:
•
•
•
A specific latitude (site location), which defines the sun-paths in relation to
the geographical location
Time of year (seasonal variation), which related to the declination of the sun
on a given day
And time of day (the earth’s rotation), which is the hourly change of the sun
from East to West
The result is a useful representation of solar patterns for clear sky conditions. Other
techniques are often used in concert with heliodon simulations to account for variations
in the strength of the sun (due to weather, angle of incidence, and atmospheric attenuation)
and local horizon shading. Heliodons provide an effective tool for the visualization and
calculation of solar effects at the window, building, or site scale.
5.2
Sunlight heliodons
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Sunlight heliodons use sunlight as the light
source, so that accurate insolation effect on
buildings can be modeled physically. (Note:
Insolation means incident solar radiation,
which affects both building heating and
lighting, and solar energy use such as solar
hot water and photovoltaic systems). For
insolation study of physical models, there is
no scaling effect needed in general. A
reasonably scaled model must be used for
the sunlight heliodon. All the actual building
components have to be in dimensionally
scaled manner including actual wall paper,
carpet, glass, furniture etc. The modeled results
will be of accuracy that our eyes normally
cannot tell the difference with the actually built
environment.
5.3
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Figure 5.2 Sunlight heliodon
Artificial light heliodons
Artificial light heliodons use artificial lights as the light source
The artificial heliodons developed so far could be broadly
categorized into three types:
•
•
•
a fixed light source (single lamp or multiple lamps),
with the building model rotated and/or tilted
the building model is placed horizontally, and the light
source moves
the building model, moves and is tilted, and the light
source also moves
While each category or type is designed on different emphasis
of its purpose of measuring certain variables, and for certain
operation convenience, the type with horizontally placed
models appear most easily understood to most people including
students, professionals, building developers and purchasers and
building users. A heliodon of this type should be basic
equipment to architectural schools.
5.4
Usefulness
Figure 5.3 Artificial light
heliodon
Sunlight affects all buildings. Ignorance of the sun's impact results in wasted energy,
overheating, glare and missed opportunities for the positive use of daylight. Awareness of
the sun's path allows for the design of shading devices, analysis of radiation impact and
the resulting energy balance, and the design of the building fenestration for optimal
utilization of daylight. It is necessary to develop a building's daylighting design before
developing the appropriate electrical lighting and switching layout.
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For all of these reasons there is a need for an effective tool like a heliodon to carry out
these issues. To date, there is not an inexpensive heliodon available that can be used as a
teaching tool. Thus, in this team project, we decided to build and design an economical
heliodon in order to aid students in better understanding of the relationship between the
sun’s path and the effects on the architecture. This economical heliodon is easy to
construct and typically costs less than S$40.00 for materials.
Even with the advances in computers, physical models are still the best predictor of how
an architectural space will perform in sunlight. Using this heliodon, one can do shading
analysis, qualitative illustration, quantitative measurements and parametric model testing.
The heliodon is an effective tool for teaching daylighting and analyzing the effects of
daylighting. In addition, once the effects of daylighting are known it is possible to
integrate electric lighting to compliment the daylighting. Modeling gives the student
freedom to try different kinds of geometry and know how they work quite immediately.
Using this tool builds enthusiasm, is simple to use, quick, and accurate. Anyone can have
access to this tool due to its inexpensive cost. Students using this tool begin to see
architecture and solar geometry in context with each other; the issues are not isolated but
are synthetically combined. This heliodon is a powerful architectural tool that can inspire
a new generation of lighting designers.
5.5
Theory and application of our Heliodon
Introduction
As mention earlier, the heliodon is a device that can
simulate the actual interaction of sunlight and the
architecture in different locations (varying latitudes), time
of the year and time of the day.
Hence, we now examine how the mechanism of our
heliodon can achieve these conditions. Our heliodon would
have to be able to simulate/vary the following 3 conditions:
1) The latitude
2) The time of the day (Hours)
3) The time of the year (Months)
1) Simulating conditions of different latitudes
The latitude can be described as the angular difference away from the equator. Given so,
the latitude at the equator is 0 degrees. The heliodon fix/assumed the 0 degree latitude
condition happens when the base board is perpendicular to the ground. (See diagram
below)
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Figure 1
0 degrees
Latitude
(Equator)
40°
40 degrees
Latitude
(Temperate)
40°
To vary the latitude, the base board is tilted away from the perpendicular position. The
angle of tilt from the perpendicular will correspond to the latitude of the simulated place.
As shown in Figure 1, the exact angle of tilt can be determined by attaching a plumb line
to the protractor mounted at the edge of the base board. The intersection of the plumb line
with the protractor will yield the latitude.
2) Simulating the time of the day.
The apparent clockwise motion of the sun is caused by the actual anti-clockwise rotation
of Earth. Hence during the experiment the base board is rotated anti-clockwise (view
from top). The horizon is the plane of the base board extended infinitely outwards. Hence,
with the tilting of the base board, the simulated
horizon follows according to the tilt of the base
board.
The sunrise on the heliodon is therefore the moment
in time where the sun (artificial light source) is first
visible with respect to the simulated horizon.
Correspondingly, the sunset is the moment in time
where the sun becomes invisible with respect to the
simulated horizon. To movement from sunrise to
sunset is thus simulated with the rotation of the
baseboard. For more precise readings of the simulated time of the day, the use of a polar
sundial is necessary (see section on polar sundial).
3) Simulating the time of the year.
June Solstice +23.5°
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Using a geocentric model, the
time of the year can be
define/known by the apparent
position of
the sun with respect to the
Earth. The diagram above illustrate how the time of the year can be derived when we
know what is the declination of the sun. Similarly, in order to obtain more precise
readings of the simulated time of the year, the use of a polar sundial is advocated.
March/September Equinoxes 0°
December Solstice -23.5°
Practical Application of the heliodon
Having understood how our heliodon works, we now focus on the practical application of
the equipment. To be specific, we will use the heliodon to analysis the building and
design consideration in the equator and temperate region.
Equator
As shown in the diagram on the left, the position of
the sun will not vary much across the year. From the
June solstice to December solstice, the sun remains
primary on top (high in the sky), with only slight
fluctuation from the zenith position in the equinoxes.
In the equatorial region, the temperature fluctuations
over the time of the year would not vary much.
Unlike the temperate region, there are no seasonal
changes in the equatorial region. Hence, the prime
concern in the building design would be the ability to
keep out the sunlight and heat to reduce the energy
consumption on artificial cooling.
Temperate
The main differences between the temperate region and the topics/equatorial region are:
a) The position of the sun in the sky varies drastically from June solstice to
December solstice.
b) The artificial heating/cooling requirements of the buildings in the region vary
drastically over the course of the year. This is due to the
fact that there are seasonal changes in the temperate
zones.
June
In June, the people living in the temperate regions are
experiencing summer (Northern Hemisphere).
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The sun is relatively high in the sky. Since it’s the summer months, the prime concern
will be to block extensive sunlight penetration. This is to reduce the heating effect the sun
rays will have on the building. Achieving this will correspondingly cut down on the
energy consumed in artificial cooling.
When it comes to excluding extensive sunlight penetration, the architects can use the
heliodon to test their various aspects of sun exclusion methods. These methods include:
1) Varying the orientation of the construction such that the sunny side of the
construction permits lowest heat transfer. For example, not building extensive
glass windows or glass wall panel on the sunny side (the side of the architecture
that faces predominantly towards the sun in the course of the day).
2) Employing and testing of sun shading devices. The heliodon can be used to assess
whether the sun shade employed is effective in blocking out the sun rays.
Shading
devices
(Overhang)
Shading devices
(Overhang/Extended
Roofing)
December
In December, it is the winter season in the Northern Hemisphere. The sun is relatively
low in the sky. In the winter months, the most important consideration in building
maintence is heating control. As large sum of energy is consumed to provide for artificial
heating, it is therefore logical and wise to tap into the sun’s energy. By allowing more
sunlight to enter the construction will provide for natural heating that aids in minimizing
the cost incurred in artificial heating.
Hence, architects can make use of the heliodon to test to see if their design allows for
adequate sunlight penetration. The testing consideration can be somewhat similar to that
of the summer months, where the designers test their proposed construction by varying
orientation, varying design and building material employed.
U
Use of glass roofing
Use of louvers
Use of Glass penal walls
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By being able to simulate the day lighting conditions in any given latitude and time,
the architects can better understand and anticipate the nature of the interaction between
sunlight and their construction. This will allow them to be able to come up with better
alterations and improvements to their designs to achieve the optimal results in building
performance.
BIBLIOGRAPHY
Kukreja, C.P. (1982). Tropical Architecture. New Delhi: McGraw –Hill.
Lam, W.M.C. (1986). Sunlighting as Formgiver for Architecture. New York: Van
Nostrand Reinhold Company.
Olgyay, A. and Olgyay, V. (1976). Solar Control and Shading Devices. New Jersey:
Princeton University Press.
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Wright, D. (1984). Natural Solar Architecture. New York: Van Nostrand Reinhold
Company.
Steemers, T.C. (1991). Solar Architecture in Europe. UK: Prism Press.
Shaw, A. (1989). Energy Design for Architects. New Jersey: Prentice-Hall.
Kemper, A.M. (1979). Architectural Handbook. USA: John Wiley and Sons.
Steermers, T.C. (1991). Solar Architecture in Europe. Singapore: Kyodo.
http://www.spot-on-sundials.co.uk
http://www.sundials.co.uk
http://www.polaris.iastate.edu
http://www.unl.ac.uk
http://arch.hku.hk
http://sundial.arch.hawaii.edu
http://lightingdesignlab.com